Other posters have already commented on the fact that, in terms of popular opinion and Soviet propaganda, the US was not seen as "the enemy" as the USSR was portrayed in America.

I did just want to make a further note and discuss the Soviet high command's view of the United States during the Cold War, particularly pertaining to the arms race:

"The Soviet leadership's tough stance was supported by supplementary information it received on the escalating military plans of the West and, especially, of the United States. Thus, in August 1951, the head of the Central Statistical Administration, V. Starovskii, sent various statistical tables to Poskrebyshev (in effect, to Stalin) which included an item under the heading "Military Expenditure of the USA in Millions of Dollars." The table showed that according to the provisional plans for 1951-1952, American military spending would come to over 64 billion dollars (almost twice the amount spent in 1949-50), a sum which would account for almost 90 percent of all central state expenditure. Moreover, referring to a secondary Cominform publication, the appendix to the table suggested that the Truman government planned to exceed even these figures by a hefty margin. Without assessing the accuracy of this information, one may merely note that it was figures of this order which were circulated at the highest levels. To the country's leaders, these statistics underlined the sudden surge in military spending of the Soviet Union's archrival." - Khlevniuk, Oleg. Cold Peace: Stalin and the Soviet Ruling Circle 1945-1953.

In other words, the buildup of military forces, including technologies (including atomic weaponry) was done as a result of the build up of American military forces/technologies and a chilling of the Cold War. The Soviets were driven by a paranoid fear of "losing out" to the Americans, and so their actions in terms of building up arms were based on this.

So if I understand what you are saying, along with other comments, is that the USSR didn't view us as the bad guy but more as the guy leading the race and they didn't want to fall too far behind? Very interesting considering the view America grew up with.

To an extent, yeah. The Soviet high command was completely consumed with keeping up with the looming American/NATO threat, and so I think their actions were more a reaction to perceived American expansionism, than an outright hatred of the enemy. To be fair, though, this could apply to the other side to some extent as well (though not as much due to American containment policy).

Russian leadership historically switched between using internal and external threats to justify their autocratic rule. During the Cold War they could not make use of an internal threat since that would imply imperfections within their system and require a public admission that a large body of Soviets did not want to be part of a communist system. This left the need to manufacture an outsider threat and the United States posed the only viable one. The stark ideological differences helped simplify the process and added a degree of credibility to the Soviet Government's actions. The Soviets were not alone in this during the Cold War, as most major powers had several instances where domestic rhetoric forced them into actions that were contrary to the best interests of the nation. Jeremi Suri's Power and Protest: Global Revolution and the Rise of Detente details several such cases.

You have the two largest kids on the block and they're ideologically opposed to each other. Both of those usually cause problems.

Is hate really the right word though? If there was true hatred then you'd think that would have lead to outright war with one another but both nations went out of their way at times to avoid full scale open warfare.